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EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT
JOSEPH L. GREATHOUSE, MAYANK DAGA AMD RESEARCH
11/20/2014
2 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
THIS TALK IN ONE SLIDE
Demonstrate how to save space and time by using the CSR format for GPU-based SpMV
Optimized GPU-based SpMV algorithm that increases memory coalescing by using LDS
14.7x faster than other CSR-based algorithms 2.3x faster than using other matrix formats
Background
4 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
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SPARSE MATRIX-VECTOR MULTIPLICATION
1.0 - 2.0 - 3.0
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- - 6.0 - -
7.0 - - 8.0 -
- 9.0 - - -
× =
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5 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
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SPARSE MATRIX-VECTOR MULTIPLICATION
1.0 - 2.0 - 3.0
- 4.0 - 5.0 -
- - 6.0 - -
7.0 - - 8.0 -
- 9.0 - - -
× =
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6 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
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SPARSE MATRIX-VECTOR MULTIPLICATION
1.0 - 2.0 - 3.0
- 4.0 - 5.0 -
- - 6.0 - -
7.0 - - 8.0 -
- 9.0 - - -
× =
22
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7 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
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SPARSE MATRIX-VECTOR MULTIPLICATION
1.0 - 2.0 - 3.0
- 4.0 - 5.0 -
- - 6.0 - -
7.0 - - 8.0 -
- 9.0 - - -
× =
22
28
18
39
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8 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
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2
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SPARSE MATRIX-VECTOR MULTIPLICATION
1.0 - 2.0 - 3.0
- 4.0 - 5.0 -
- - 6.0 - -
7.0 - - 8.0 -
- 9.0 - - -
× =
22
28
18
39
18
9 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
1
2
3
4
5
SPARSE MATRIX-VECTOR MULTIPLICATION
1.0 - 2.0 - 3.0
- 4.0 - 5.0 -
- - 6.0 - -
7.0 - - 8.0 -
- 9.0 - - -
× =
22
28
18
39
18
10 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
1
2
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SPARSE MATRIX-VECTOR MULTIPLICATION
Traditionally Bandwidth Limited
1.0 - 2.0 - 3.0
- 4.0 - 5.0 -
- - 6.0 - -
7.0 - - 8.0 -
- 9.0 - - -
× =
22
28
18
39
18
11 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
COMPRESSED SPARSE ROW (CSR)
1.0 - 2.0 - 3.0
- 4.0 - 5.0 -
- - 6.0 - -
7.0 - - 8.0 -
- 9.0 - - -
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 values:
12 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
COMPRESSED SPARSE ROW (CSR)
1.0 - 2.0 - 3.0
- 4.0 - 5.0 -
- - 6.0 - -
7.0 - - 8.0 -
- 9.0 - - -
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 values:
13 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
COMPRESSED SPARSE ROW (CSR)
1.0 - 2.0 - 3.0
- 4.0 - 5.0 -
- - 6.0 - -
7.0 - - 8.0 -
- 9.0 - - -
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
0 2 4 1 3 2 0 3 1 columns:
values:
14 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
COMPRESSED SPARSE ROW (CSR)
1.0 - 2.0 - 3.0
- 4.0 - 5.0 -
- - 6.0 - -
7.0 - - 8.0 -
- 9.0 - - -
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
0 2 4 1 3 2 0 3 1 columns:
values:
15 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
COMPRESSED SPARSE ROW (CSR)
1.0 - 2.0 - 3.0
- 4.0 - 5.0 -
- - 6.0 - -
7.0 - - 8.0 -
- 9.0 - - -
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
0 2 4 1 3 2 0 3 1
0 3 5 6 8 9 row delimiters:
columns:
values:
16 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
COMPRESSED SPARSE ROW (CSR)
1.0 - 2.0 - 3.0
- 4.0 - 5.0 -
- - 6.0 - -
7.0 - - 8.0 -
- 9.0 - - -
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
0 2 4 1 3 2 0 3 1
0 3 5 6 8 9 row delimiters:
columns:
values:
17 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
COMPRESSED SPARSE ROW (CSR)
1.0 - 2.0 - 3.0
- 4.0 - 5.0 -
- - 6.0 - -
7.0 - - 8.0 -
- 9.0 - - -
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
0 2 4 1 3 2 0 3 1
0 3 5 6 8 9 row delimiters:
columns:
values:
18 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
AMD GPU MEMORY SYSTEM
L1 L1 L1 L1 L1 L1 L1 L1
L2
64-bit Dual Channel Memory
Controller
I$ K$ I$ K$
L2
64-bit Dual Channel Memory
Controller
L2
64-bit Dual Channel Memory
Controller
19 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
AMD GPU MEMORY SYSTEM
L1 L1 L1 L1 L1 L1 L1 L1
L2
64-bit Dual Channel Memory
Controller
64 Bytes per clock L1 bandwidth per CU
I$ K$ I$ K$
L2
64-bit Dual Channel Memory
Controller
L2
64-bit Dual Channel Memory
Controller
20 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
AMD GPU MEMORY SYSTEM
L1 L1 L1 L1 L1 L1 L1 L1
L2
64-bit Dual Channel Memory
Controller
64 Bytes per clock L1 bandwidth per CU
I$ K$ I$ K$
64 Bytes per clock L2 bandwidth per partition
L2
64-bit Dual Channel Memory
Controller
L2
64-bit Dual Channel Memory
Controller
21 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
AMD GPU MEMORY SYSTEM
L1 L1 L1 L1 L1 L1 L1 L1
L2
64-bit Dual Channel Memory
Controller
64 Bytes per clock L1 bandwidth per CU
I$ K$ I$ K$
64 Bytes per clock L2 bandwidth per partition
L2
64-bit Dual Channel Memory
Controller
L2
64-bit Dual Channel Memory
Controller
Uncoalesced accesses are much
less efficient!
22 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
Local Data Share (64KB)
Vector Registers (4x 64KB)
Vector Units (4x SIMD-16)
L1 Cache (16 KB)
AMD GPU COMPUTE UNIT
23 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
Local Data Share (64KB)
Vector Registers (4x 64KB)
Vector Units (4x SIMD-16)
L1 Cache (16 KB)
AMD GPU COMPUTE UNIT
Must do parallel loads to maximize
bandwidth
24 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
LOCAL DATA SHARE (LDS) MEMORY
Scratchpad (software-addressed) on-chip cache
Statically divided between all workgroups in a CU
Highly ported to allow scatter/gather (uncoalesced) accesses
Local Data Share (64KB)
25 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-SCALAR
One thread/work-item per matrix row
26 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-SCALAR
One thread/work-item per matrix row
Workgroup #1
Workgroup #2
Workgroup #3
27 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-SCALAR
One thread/work-item per matrix row
Workgroup #1
Workgroup #2
Workgroup #3
28 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-SCALAR
One thread/work-item per matrix row
Workgroup #1
Workgroup #2
Workgroup #3
Uncoalesced accesses
29 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-VECTOR
One workgroup (multiple threads) per matrix row
30 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-VECTOR
One workgroup (multiple threads) per matrix row
Workgroup #1
Workgroup #2
Workgroup #12
.
.
.
31 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-VECTOR
One workgroup (multiple threads) per matrix row
Workgroup #1
Workgroup #2
Workgroup #12
.
.
.
32 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-VECTOR
One workgroup (multiple threads) per matrix row
Workgroup #1
Workgroup #2
Workgroup #12
.
.
.
Good: coalesced accesses
33 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-VECTOR
One workgroup (multiple threads) per matrix row
Workgroup #1
Workgroup #2
Workgroup #12
.
.
.
34 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-VECTOR
One workgroup (multiple threads) per matrix row
Workgroup #1
Workgroup #2
Workgroup #12
.
.
.
Bad: poor parallelism
35 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
MAKING GPU SPMV FAST
Neither CSR-Scalar nor CSR-Vector offer ideal performance.
CSR works well on CPUs and is widely used
Traditional solution: new matrix storage format + new algorithms
‒ ELLPACK/ITPACK, BCSR, DIA, BDIA, SELL, SBELL, ELL+COO Hybrid, many others
‒ Auto-tuning frameworks like clSpMV try to find the best format for each matrix
‒ Can require more storage space or dynamic transformation overhead
Can we find a good GPU algorithm that does not modify the original CSR data?
CSR-Adaptive
37 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
INCREASING BANDWIDTH EFFICIENCY
38 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
INCREASING BANDWIDTH EFFICIENCY
39 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
INCREASING BANDWIDTH EFFICIENCY
CSR-Vector coalesces long rows by streaming into the LDS
40 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-VECTOR USING THE LDS
Local Data Share
41 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-VECTOR USING THE LDS
Local Data Share
42 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-VECTOR USING THE LDS
Local Data Share
43 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-VECTOR USING THE LDS
Local Data Share
44 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-VECTOR USING THE LDS
Local Data Share
+ + + +
45 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-VECTOR USING THE LDS
Local Data Share
+ + + +
Fast uncoalesced
accesses!
46 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-VECTOR USING THE LDS
Local Data Share
47 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-VECTOR USING THE LDS
Local Data Share
Fast accesses everywhere
48 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
INCREASING BANDWIDTH EFFICIENCY
How can we get good bandwidth for other “short” rows?
49 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
INCREASING BANDWIDTH EFFICIENCY
Load these into the LDS
How can we get good bandwidth for other “short” rows?
50 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-STREAM: STREAM MATRIX INTO THE LDS
Local Data Share
51 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-STREAM: STREAM MATRIX INTO THE LDS
Local Data Share
52 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-STREAM: STREAM MATRIX INTO THE LDS
Block 1 Block 2 Block 3 Block 4
Local Data Share
53 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-STREAM: STREAM MATRIX INTO THE LDS
Block 1 Block 2 Block 3 Block 4
Local Data Share
54 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-STREAM: STREAM MATRIX INTO THE LDS
Block 1 Block 2 Block 3 Block 4
Local Data Share
55 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-STREAM: STREAM MATRIX INTO THE LDS
Block 1 Block 2 Block 3 Block 4
Local Data Share
56 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-STREAM: STREAM MATRIX INTO THE LDS
Block 1 Block 2 Block 3 Block 4
Local Data Share
57 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-STREAM: STREAM MATRIX INTO THE LDS
Block 1 Block 2 Block 3 Block 4
Local Data Share
58 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-STREAM: STREAM MATRIX INTO THE LDS
Block 1 Block 2 Block 3 Block 4
Local Data Share
Fast accesses everywhere
59 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
FINDING BLOCKS FOR CSR-STREAM
0 3 6 8 10 14 16 17 19 20 22 24 32
row delimiters:
values:
DONE ONCE ON THE CPU
columns:
60 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
FINDING BLOCKS FOR CSR-STREAM
0 3 6 8 10 14 16 17 19 20 22 24 32
row delimiters:
values:
DONE ONCE ON THE CPU
columns:
61 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
FINDING BLOCKS FOR CSR-STREAM
row delimiters:
values:
DONE ONCE ON THE CPU
columns:
62 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
FINDING BLOCKS FOR CSR-STREAM
row delimiters:
values:
0 3 6 11 12
row blocks:
DONE ONCE ON THE CPU
Assuming 8 LDS entries per workgroup
columns:
63 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
FINDING BLOCKS FOR CSR-STREAM
row delimiters:
values:
0 3 6 11 12
row blocks:
DONE ONCE ON THE CPU
Assuming 8 LDS entries per workgroup
columns:
64 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
FINDING BLOCKS FOR CSR-STREAM
row delimiters:
values:
0 3 6 11 12
row blocks:
DONE ONCE ON THE CPU
Assuming 8 LDS entries per workgroup
columns:
65 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
FINDING BLOCKS FOR CSR-STREAM
row delimiters:
values:
0 3 6 11 12
row blocks:
DONE ONCE ON THE CPU
Assuming 8 LDS entries per workgroup
columns:
66 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
FINDING BLOCKS FOR CSR-STREAM
row delimiters:
values:
0 3 6 11 12
row blocks:
Block 1
DONE ONCE ON THE CPU
Assuming 8 LDS entries per workgroup
columns:
67 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
FINDING BLOCKS FOR CSR-STREAM
row delimiters:
values:
0 3 6 11 12
row blocks:
Block 1 Block 2
DONE ONCE ON THE CPU
Assuming 8 LDS entries per workgroup
columns:
68 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
FINDING BLOCKS FOR CSR-STREAM
row delimiters:
values:
0 3 6 11 12
row blocks:
Block 1 Block 2 Block 3 Block 4
DONE ONCE ON THE CPU
Assuming 8 LDS entries per workgroup
columns:
69 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
FINDING BLOCKS FOR CSR-STREAM
row delimiters:
values:
0 3 6 11 12
row blocks:
Block 1 Block 2 Block 3 Block 4
CSR Structure Unchanged
DONE ONCE ON THE CPU
Assuming 8 LDS entries per workgroup
columns:
70 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
WHAT ABOUT VERY LONG ROWS?
Local Data Share
71 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
WHAT ABOUT VERY LONG ROWS?
Block 1 Block 2
Local Data Share
Block 3
72 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
WHAT ABOUT VERY LONG ROWS?
Block 1 Block 2 Block 4
Local Data Share
Block 3
73 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
WHAT ABOUT VERY LONG ROWS?
Block 1 Block 2 Block 4
Local Data Share
CSR-Stream
Block 3
74 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
WHAT ABOUT VERY LONG ROWS?
Block 1 Block 2 Block 4
Local Data Share
CSR-Stream CSR-Vector
Block 3
75 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
WHAT ABOUT VERY LONG ROWS?
Block 1 Block 2 Block 4
CSR-Stream CSR-Vector
Block 3
CSR-Adaptive
76 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-ADAPTIVE
77 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-ADAPTIVE
(Once per matrix) On CPU: Create Row
Blocks
78 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-ADAPTIVE
(Once per matrix) On CPU: Create Row
Blocks
On GPU (each workgroup assigned one row block):
Read Row Block Entries
79 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-ADAPTIVE
(Once per matrix) On CPU: Create Row
Blocks
On GPU (each workgroup assigned one row block):
Read Row Block Entries
Single Row?
80 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-ADAPTIVE
(Once per matrix) On CPU: Create Row
Blocks
On GPU (each workgroup assigned one row block):
Read Row Block Entries
Single Row?
CSR-Vector Yes
81 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-ADAPTIVE
(Once per matrix) On CPU: Create Row
Blocks
On GPU (each workgroup assigned one row block):
Read Row Block Entries
Single Row?
CSR-Vector
Vector Load Row into LDS
Perform Parallel Reduction out of LDS
Yes
82 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-ADAPTIVE
(Once per matrix) On CPU: Create Row
Blocks
On GPU (each workgroup assigned one row block):
Read Row Block Entries
Single Row?
CSR-Vector CSR-Stream
Vector Load Row into LDS
Perform Parallel Reduction out of LDS
Yes No
83 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CSR-ADAPTIVE
(Once per matrix) On CPU: Create Row
Blocks
On GPU (each workgroup assigned one row block):
Read Row Block Entries
Single Row?
CSR-Vector CSR-Stream
Vector Load Multiple Rows into LDS
Perform Reduction out of LDS (serially or in parallel)
Vector Load Row into LDS
Perform Parallel Reduction out of LDS
Yes No
Experiments
85 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
EXPERIMENTAL SETUP
CPU: AMD A10-7850K (3.7 GHz)
‒ 32 GB dual-channel DDR3-2133
GPU: AMD FirePro™ W9100
‒ 44 parallel compute units (CUs)
‒ 930 MHz core clock rate (5.2 single-precision TFLOPs)
‒ 16 GDDR5 channels at 1250 MHz (320 GB/s)
CentOS 6.4 (kernel 2.6.32-358.23.2)
‒ AMD FirePro Driver version 14.20 beta
‒ AMD APP SDK v2.9
86 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
SPMV SETUP
SHOC Benchmark Suite (Aug. 2013 version)
‒ CSR-Vector (details in paper: CSR-Scalar, ELLPACK)
ViennaCL v1.5.2
‒ CSR-Scalar, COO, ELLPACK, ELLPACK+COO HYB
‒ 4-value and 8-value padded versions of CSR-Scalar
‒ Best of these for each matrix: “ViennaCL Best”
clSpMV v0.1
‒ CSR-Scalar, CSR-Vector, BCSR, COO, DIA, BDIA, ELLPACK, SELL, BELL, SBELL
‒ Best of these for each matrix: “clSpMV Best”
‒ Details in paper: clSpMV “Cocktail” format
CSR-Adaptive
20 matrices from Univ. of Florida Sparse Matrix Collection
87 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
DATA STRUCTURE GENERATION TIMES
1
2
4
8
16
32
64
128
256
512
1024
Ge
ne
rati
on
tim
e v
s. C
OO
→C
SR
Row Blocking ELLPACK BCSR Cocktail
Note: Some matrices could not be held in ELLPACK or BCSR
88 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
PERFORMANCE IN SINGLE-PRECISION GFLOPS
89 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
PERFORMANCE IN SINGLE-PRECISION GFLOPS
0
10
20
30
40
50
60
70
80
90
GFL
OP
S (S
ingl
e P
reci
sio
n)
Roughly Equal Performance (7/20)
90 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
PERFORMANCE IN SINGLE-PRECISION GFLOPS
0
10
20
30
40
50
60
70
80
90
GFL
OP
S (S
ingl
e P
reci
sio
n)
Roughly Equal Performance (7/20)
91 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
PERFORMANCE IN SINGLE-PRECISION GFLOPS
0
10
20
30
40
50
60
70
80
90
GFL
OP
S (S
ingl
e P
reci
sio
n)
110.7 Roughly Equal Performance (7/20) Others Better (4/20)
92 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
PERFORMANCE IN SINGLE-PRECISION GFLOPS
0
10
20
30
40
50
60
70
80
90
GFL
OP
S (S
ingl
e P
reci
sio
n)
110.7 Roughly Equal Performance (7/20) Others Better (4/20)
93 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
PERFORMANCE IN SINGLE-PRECISION GFLOPS
0
10
20
30
40
50
60
70
80
90
GFL
OP
S (S
ingl
e P
reci
sio
n)
CSR-Adaptive Performance Higher (9/20)
94 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
PERFORMANCE BENEFIT OF CSR-ADAPTIVE
0
5
10
15
20
25
30
35
CSR-Scalar CSR-Vector ELLPACK ViennaCLBest
clSpMVCocktail
clSpMV BestSingle
CSR
-Ad
apti
ve S
pe
ed
up
95 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CONCLUSION
CSR-Adaptive up to 14.7x faster than previous GPU-based SpMV algorithms
Requires little work beyond generating the traditional CSR data structure
‒ Less than 0.1% extra storage compared to CSR
Algorithm is not complex: easy to integrate into libraries and existing SW
96 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CONCLUSION
CSR-Adaptive up to 14.7x faster than previous GPU-based SpMV algorithms
Requires little work beyond generating the traditional CSR data structure
‒ Less than 0.1% extra storage compared to CSR
Algorithm is not complex: easy to integrate into libraries and existing SW
AMD Sample Code Available Soon – Ask Us!
97 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
CONCLUSION
CSR-Adaptive up to 14.7x faster than previous GPU-based SpMV algorithms
Requires little work beyond generating the traditional CSR data structure
‒ Less than 0.1% extra storage compared to CSR
Algorithm is not complex: easy to integrate into libraries and existing SW
AMD Sample Code Available Soon – Ask Us!
Independently Implemented Version in
ViennaCL 1.6.1
98 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
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ATTRIBUTION
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Backup Slides
100 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
AMD GPU MICROARCHITECTURE
101 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
AMD GPU MICROARCHITECTURE
102 | EFFICIENT SPARSE MATRIX-VECTOR MULTIPLICATION ON GPUS USING THE CSR STORAGE FORMAT | NOVEMBER 20, 2014
AMD GPU MICROARCHITECTURE